write an algebraic expression for the nth term of this sequence.
7, 11, 16, 22,...
I know what algebraic expression is.
Well, aren't you a smarty pants! Alright, let me give it a try:
To find the nth term in this sequence, it seems like each subsequent term is getting bigger and bigger. So, let's break it down.
If we look at the difference between each term, we can see that it is increasing by 4. For the first term, the difference is 4, for the second term, the difference is 5, and so on.
So, we can say that the pattern is increasing by 1 each time. And if we subtract this pattern from the previous term, we'll get the next term.
To express this mathematically, we start with the first term which is 7, and then we say that the nth term is 7, plus (n-1) times 1, since the difference increases by 1 each time.
Therefore, the algebraic expression for the nth term in this sequence is 7 + (n-1) * 1.
Now, wasn't that algebraic expression a piece of cake?
To find the algebraic expression for the nth term of the sequence 7, 11, 16, 22, ..., you can start by observing the pattern in the sequence. The difference between consecutive terms is increasing by 1 each time (4, 5, 6, ...).
Let's break it down step-by-step:
Step 1: Determine the difference between consecutive terms:
11 - 7 = 4
16 - 11 = 5
22 - 16 = 6
Step 2: Observe that the difference is increasing by 1 each time.
Step 3: Write the algebraic expression using the first term and the common difference. Let's use 'n' to represent the position of the term in the sequence:
First Term + (n - 1) * Common Difference
Substitute the first term (7) and the common difference (4) into the expression:
7 + (n - 1) * 4
Simplify the expression:
7 + 4n - 4
Combine like terms:
4n + 3
Therefore, the algebraic expression for the nth term of the sequence 7, 11, 16, 22, ... is 4n + 3.
To find the algebraic expression for the nth term of a sequence, we first need to observe the pattern in the sequence. In this case, we notice that each term is increasing by a consistent amount.
The difference between each pair of consecutive terms is:
11 - 7 = 4
16 - 11 = 5
22 - 16 = 6
We can see that the difference between the terms is increasing by 1 each time. This indicates that the sequence itself is increasing by 1 each time.
Now, let's denote the first term of the sequence as "a" and the common difference between terms as "d".
The first term, a = 7
The common difference, d = 1
To find the algebraic expression, we can use the formula for arithmetic sequences:
nth term = a + (n - 1)d
Plugging in the values we have:
nth term = 7 + (n - 1)(1)
Simplifying the expression, we get:
nth term = 7 + n - 1
Combining like terms, we get:
nth term = n + 6
Therefore, the algebraic expression for the nth term of the sequence 7, 11, 16, 22, ... is n + 6.
note that the differences are 4,5,6
Now, you know that 1+2+3+...+n = n(n+1)/2
Your sequence is 7 + 4+5+6+...
see what you can do with that